Full-time from the Keepmoat Stadium
Morison got his side of to a dream start, clipping a sublime chip over the head of Rovers keeper Thorsten Stuckmann after just six minutes, only for former Lion Richard Chaplow to slot home Andy Williams' pull-back and level eight minutes before half-time.
Although this was not a vintage performance from The Lions, this could yet prove to be a vital point come the end of the season with promotion rivals Coventry, Southend, Gillingham and Sheffield United all slipping up.
The game started at a cracking pace with both goalkeeper, Jordan Archer and Stuckmann racing off their line to clear from Conor Grant and Lee Gregory respectively.
Ben Thompson saw a smart shot deflected wide for a corner on four minutes with the first effort on goal and although Shane Ferguson's delivery was cleared, The Lions didn't have long to wait to break the deadlock.
Barely two minutes later an error by Paul Keegan let in Morison, and the frontman used great skill and guile to loft the ball over the onrushing Stuckmann and into the back of the net.
Doncaster threatened with a couple of inviting deliveries, the first from Cedric Evina that Archer collected comfortably and the second, a flat cross from Aaron Taylor-Sinclair that the keeper allowed to travel out for a goal kick.
A slick counter attack on 14 minutes provided a timely reminder that The Lions were a threat too, as Mahlon Romeo, Jed Wallace, Morison and Ferguson linked up superbly before the latter's cross was cleared.
Millwall had a cast iron penalty turned down on 29 minutes when Gregory clearly had his shirt clearly pulled as he tried to get clear of Luke McCullough inside the danger zone. The striker still managed to squeeze a shot in that Stuckmann parried for a corner.
Ferguson's first delivery was cleared for another corner before a second - taken short - just evaded the head of defender Byron Webster at the back post.
Doncaster, who had been restricted to long-range efforts from Keegan and a 25-yarder from Grant, conjured up an equaliser out of the blue seven minutes before the break. A determined run by Williams down the right took him clear of two players and his low cross was lashed home by Chaplow from close range.
The home side really had the bit between their teeth now and it took a fine 43rd-minute save by Archer at full stretch to keep deny Chaplow his second goal two minutes before the break of a half that had started so promisingly for The Lions, but ended with Doncaster in the ascendancy.
Millwall had a great opportunity to restore the lead within four minutes of the restart when Gregory rolled his marker and picked out Morison, standing barely two yards out with the goal at his mercy. An unfortunate combination of the ball bobbling just as he tried to connect saw the captain completely miss the cross and the chance had gone.
Former Lion Chaplow was the first name in referee Boyseon's book for a late 54th-minute challenge that left Webster needing treatment before Webster himself was shown a yellow card for a foul on Nathan Tyson moments after returning to the field of play.
Both teams tried to build up a head of steam with plenty of effort and endeavour - and half chances too. Wallace was a fraction away from connecting with an inviting Ferguson delivery whilst at the other end Evina sliced wide from a good position.
Gregory broke clear on 66 minutes, but his effort was gratefully gathered by keeper Stuckmann and then Taylor-Sinclair's flick was met by the head of sub Lynden Gooch, who steered his effort wide of the target as the two teams continued to probe and prise in a bid to get that second, all important goal.
Ferguson drilled a left-foot shot a yard wide with his last contribution before being replaced by Aiden O'Brien to add some fresh legs and impetus in attack, but it was Doncaster who so nearly edged ahead with eight minutes remaining. Tyson looked odds on to score when he was clean through on goal, only to be denied by a superb reflex save from Archer at close range.
At the other end, Stuckmann showed a safe pair of hands to grab Webster's firm header from a corner as Millwall tried to find a way through.
On came Fred Onyedinma for The Lions as the game headed towards injury-time and Gregory's forward charge was brought to an abrupt halt by McCullough, who earned a booking for hauling the striker to the ground.
However it was the home side who so nearly snatched all three points right at the death when Grant raced through and saw his angled goalbound shot brilliantly turned away by Archer for a corner which was cleared, with referee Boyeson blowing for full-time seconds later.
Doncaster Rovers: Stuckmann, Lund, Evina, McCullough, Chaplow, Williams (Gooch, 60mins), Tyson, Keegan (Middleton, 52mins), Taylor-Sinclair, Grant, Alcock. Subs not used: Butler, Mandeville, Marosi, Coppinger, Stewart.
Bookings: Chaplow (54mins), Grant (55mins), McCullough (90+1min)
Scorer: Chaplow (37mins)
Millwall: Archer, Romeo, Marti, Beevers, Webster, Adbou, Thompson, Ferguson (O'Brien, 76mins), Gregory, Morison, Wallace (Onyedinma, 88mins). Subs not used: Forde, Williams, Nelson, Philpot, Mbulu.
Bookings: Webster (56mins), Thompson (79mins)
Scorer: Morison (6mins)
Ref: C. Boyeson
Att: 6,810 (away 825)